드리다 is the humble counterpart of 주다 'give, do for', used when the recipient outranks you, and -고 links the action that comes before it. Three lines here are 보고(를) 드리다, 'to report to a superior' — 본부장님까지 보고드리고. Others are ordinary offers made politely: 이렇게 해가지고 드릴게요, 'I'll make it and give it to you'.